Ok, we all know that the N64 is one tricky system to portablize, mainly because of how finicky it is. Even Ben had trouble on it! Many times, an N64 will suddenly stop working. Now, it COULD be fried...but usually, it's just, for lack of a better word, "sleeping"
First of all, before getting into the troubleshooting, get yourself an anti-static wrist band or touch a metal pipe or metal computer case connected to ground to get rid of static everytime you handle your N64. Try to handle it by the sides, too.
To wake your N64 up, go through the following steps (let's see if I can remember 'em...):
1. Check the power. First, make sure none of the power pins are shorted or somehow touching each other. Make sure you've got 3.3V on the 3.3V line, and at least 7.2V on the 12V line (goes to a 7805). If you don't, and you're using the original power supply, keep it unplugged for a day and then plug it in and try it. If you're still not getting power, try a new one. If you're using an alternative source of power, make sure that the 3.3V supplier can do at least 1.5A, and that the 7.2V or higher supplier can do above 100mA or so. Once you have the proper power going into the system, check that the 7805 (on the side with the chips) is outputting 5V. Turn on the system, and hope it works...
2. If it still doesn't work, check the video lines to make sure that they're going into the screen or TV that you're using and that ground is connected. Ground can be found on the metal strips on the side of the N64. The video line is 9, I believe. If video works, try audio, (left is pin 11, right is pin 12. For mono, just use pin 11).
3. If it's still not working (which, if you usually don't screw up wiring, is quite likely) then there's still a method to get it to work. First, take everything out, the game and the expansion pack. Turn it on for 10 seconds or so, and then turn it off. Plug in the expansion/jumper pack (make sure it's in the right way...I believe the main pins go towards the center of the motherboard), turn it on for ten seconds, and then shut if off again. Blow or clean the cartridge, and then do the same for the cart. slot, and push the game in hard enough to make sure it's secure in the cart. slot (once again, have it in the right way!). Now try it. If it still doesn't work, try cleaning the game or use a different game. After that, if still not working, repeat steps 1-3 and try again. If after all this it's still not working, check to make sure that the TV or screen is working (use a different system to output the video). If your N64 is still not working, then just leave it in a non-humid area for a week, and come back and troubleshoot.
-If you rewired the cart. slot, make sure each pin goes to the corresponding area on the mobo. Then, make sure no pins are touching each other.
-Check for little specks of solder that could be shorting something on the board. If it's on one of the main chips, that could ruin the N64, but if it's on a smaller component, just remove or desolder it, and try again.
-try a new expansion pack or jumper pack (using the method in step 3 to get it to work).
-Make sure no little smt components popped off. It's hard to troubleshoot for this, because of the small size of smt components, but it's worth a try.
-Make sure the power switch works...
-Um, perhaps try replacing that red LED...I'm not sure if it's an importnat part of the power circuit, but try anyway, if you're still stuck.